Investigation of the critical properties of the frustrated Heisenberg model on a triangular lattice by the Monte Carlo method

The critical properties of the 3D frustrated antiferromagnetic Heisenberg model on a triangular lattice have been investigated by the replica Monte Carlo method. All main magnetic and chiral critical indices were calculated using the finite-size scaling theory. It is found that the class of universality of the critical behavior of the model studied depends on the type of interplane exchange interaction.     

Monte Carlo investigation of phase transitions in the frustrated Heisenberg model on a triangular lattice

The critical properties and phase transitions of the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice have been investigated using the Monte Carlo method with a replica algorithm. The critical temperature has been determined and the character of the phase transitions has been analyzed using the method of fourth-order Binder cumulants. A second-order phase transition has been found in the three-dimensional frustrated Heisenberg model on a triangular lattice. The static magnetic and chiral critical exponents of the heat capacity α, the susceptibility γ and γ _k , the magnetization β and β _k , the correlation length ν and ν _k , as well as the Fisher exponents η and η _k , have been calculated in terms of the finite-size scaling theory. It has been demonstrated that the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice forms a new universality class of the critical behavior.     

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice with allowance for intralayer next nearest neighbor interactions have been studied using the replica Monte Carlo algorithm. The character of phase transitions has been analyzed using the histogram method and the Binder cumulant method. It has been found that a transition from the collinear to paramagnetic phase in the model under study occurs as a second order phase transition. The statistical critical exponents of the specific heat α, susceptibility γ, order parameter β, and correlation radius ν, as well as the Fisher index η, have been calculated using the finite-size scaling theory. It has been shown that the three-dimensional Heisenberg model on the layered cubic lattice with allowance for the next nearest neighbor interaction belongs to the same universality class of the critical behavior as the antiferromagnetic Heisenberg model on a layered triangular lattice.     

Ising-type critical exponents of the fully frustrated spin-1/2 Heisenberg FM/AF square bilayer at a critical magnetic field

The fully frustrated spin-1/2 Heisenberg FM/AF square bilayer in a magnetic field with the ferromagnetic inter-dimer interaction and the antiferromagnetic intra-dimer interaction is explored by the use of localized many-magnon approach, which allows to connect the original purely quantum Heisenberg spin model on a square bilayer with the effective ferromagnetic Ising model on a simple square lattice. Magnetization and specific heat are investigated exactly at a field-driven phase transition from the singlet-dimer phase towards the fully saturated ferromagnetic phase, which changes from a discontinuous phase transition to a continuous one at a certain critical temperature. The mapping correspondence between the spin-1/2 Heisenberg FM/AF square bilayer and the ferromagnetic Ising square lattice suggests for this special critical point of the spin-1/2 Heisenberg FM/AF square bilayer critical exponents from the standard two-dimensional Ising universality class.     

Critical behavior and spatial crossover in the frustrated antiferromagnetic Heisenberg model on a triangular lattice

The critical properties of the three-dimensional frustrated Heisenberg model on a layered triangular lattice with variable interplane exchange interaction have been investigated by the replica Monte Carlo method. All main magnetic and chiral critical exponents have been calculated. It is found that a decrease in the interlayer exchange leads to crossover from the three-to two-dimensional critical behavior.     

Static critical behavior of 3D frustrated Heisenberg model on stacked triangular lattice with variable interlayer exchange coupling

Several Monte Carlo algorithms are used to examine the critical behavior of the 3D frustrated Heisenberg model on stacked triangular lattice with variable interlayer exchange coupling for values of the interlayer-to-intralayer exchange ratio R = |′/J| in the interval between 0.01 and 1.0. A finite-size scaling technique is used to calculate the static magnetic and chiral critical exponents α (specific heat), γ and γ_k (susceptibility), β and β_k(magnetization), ν and ν_k(correlation length), and the Fisher exponent η. It is shown that 3D frustrated Heisenberg models on stacked triangular lattice with R > 0.05 constitute a new universality class of critical behavior. At lower R, a crossover from 3D to 2D critical behavior is observed.     

Phase transitions and critical properties of the frustrated Heisenberg model on a layer triangular lattice with next-to-nearest-neighbor interactions

The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J ₁) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = |J ₁/J| = 0?C0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.     

Critical properties of a frustrated Heisenberg model on a stacked triangular lattice with allowance for second-nearest neighbor interaction

The critical properties of the three-dimensional antiferromagnetic Heisenberg model are investigated using the Monte Carlo method with allowance for second-nearest neighbor interaction. Pseudo-universal critical behavior of this model is observed for small lattices. A complete set of the main static magnetic and chiral indices is calculated with the use of finite-dimensional scaling theory.     

Spin 1 frustrated antiferromagnet with biquadratic exchange and single ion anisotropy

The zero temperature properties, using the bond operator technique, are determined for the frustrated S=1 Heisenberg antiferromagnetic model plus nearest-neighbor biquadratic exchange interaction and single ion anisotropy on a two dimensional square lattice.     

Green’s function approach to the low temperature properties of Cs<Subscript>2</Subscript>CuCl<Subscript>4</Subscript>: anisotropy effects

We have studied the effect of both axial and transverse anisotropy on the critical field and thermodynamic properties of the field induced three dimensional antiferromagnetic Heisenberg model on the frustrated hexagonal lattice for Cs₂CuCl₄ compound. The spin model is mapped to a bosonic one with the hard core repulsion constraint and the Green’s function approach has been implemented to get the low energy spectrum and the corresponding thermodynamic properties. To find the critical field (B _c ) we have looked for the Bose-Einstein condensation of quasi-particles (magnons) which takes place when the magnon spectrum vanishes at the ordering spiral wave vector. We have also obtained the dispersion of magnon spectrum in the critical magnetic field for each anisotropy parameter to find the spiral wave vector where the spectrum gets its minimum. The magnon energies show a linear dispersion relation close to the quantum critical point. The effect of hard core boson interaction on the single particle excitation energies leads to a temperature dependence of the magnon spectrum versus magnetic field. We have also studied the behavior of specific heat and static structure factor versus temperature and magnetic field.     

Critical properties of the three-dimensional frustrated Ising model on a cubic lattice

The critical properties of the three-dimensional fully frustrated Ising model on a cubic lattice are investigated by the Monte Carlo method. The critical exponents α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length), as well as the Fisher exponent η, are calculated in the framework of the finite-size scaling theory. It is demonstrated that the three-dimensional frustrated Ising model on a cubic lattice forms a new universality class of the critical behavior.     

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.     

Thermodynamic properties of Heisenberg model for magnetic ordered graphene sheet

We study the thermodynamic properties of two dimensional Heisenberg antiferromagnet on the honeycomb lattice in the presence of anisotropic Dzyaloshinskii-Moriya interaction and next nearest neighbor coupling exchange constant. A sublattice antiferromagnetic long range ordering has been considered for localized electrons on honeycomb lattice structure. In particular, the temperature dependence of specific heat has been investigated for various physical parameters in the model Hamiltonian. Using Holstein-Primakoff bosonic transformations, the behavior of thermodynamic properties has been studied by means of excitation spectrum of mapped bosonic gas. Furthermore we have studied the dependence of specific heat and magnetization on Dzyaloshinskii-Moriya interaction strength for various next nearest neighbor interaction strengths. At low temperatures, the specific heat is found to be monotonically increasing with temperature. We have found the dependence of specific heat on Dzyaloshinskii-Moriya interaction strength shows a monotonic increasing behavior for various next nearest neighbor exchange constants. Also we have studied the temperature dependence of staggered magnetization for different next nearest neighbor coupling constants. Our results show the critical temperature moves to higher amounts with reduction of Dzyaloshinskii-Moriya interaction strength.     

Critical properties of the antiferromagnetic layered Ising model on a cubic lattice with competing interactions

The critical properties of the antiferromagnetic layered Ising model on a cubic lattice with regard to the nearest-neighbor and next-nearest-neighbor interactions are investigated by the Monte Carlo method using the replica algorithm. The investigations are carried out for the ratios of exchange nearest-neighbor and next-nearest-neighbor interactions r = J ₂/J ₁ in the range of 0 ≤ r ≤ 1.0. Using the finite-size scaling theory, the static critical indices of specific heat α, order parameter β, susceptibility γ, correlation radius ν, and Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is retained in the range of 0 ≤ r ≤ 0.4. It is established that the change in the next-nearest-neighbor interaction value in this model in the range of r > 0.8 leads to the same universality class as the three-dimensional fully frustrated Ising model on the cubic lattice.

     

Direct determination of the magnetic ground state in the square lattice S = 1/2 antiferromagnet Li2VOSiO4

Powder neutron diffraction and resonant x-ray scattering measurements from a single crystal have been performed to study the low-temperature state of the 2D frustrated, quantum-Heisenberg system Li2VOSiO4. Both techniques indicate a collinear antiferromagnetic ground state, with propagation vector k=(1 / 2 1 / 2 0), and magnetic moments in the a-b plane. Contrary to previous reports, the ordered moment at 1.44 K, m=0.63(3)micro(B), is very close to the value expected for the square lattice Heisenberg model ( approximately 0.6micro(B)). The magnetic order is three dimensional, with antiferromagnetic a-b layers stacked ferromagnetically along the c axis. Neither x-ray nor neutron diffraction shows evidence for a structural distortion between 1.6 and 10 K.     

三维钻石型等级晶格上量子Heisenberg系统的临界性质

利用重整化群方法,研究了三维钻石型等级晶格上的各向异性量子Heisenberg模型,获得了系统的相图和临界性质. 结果表明:对于铁磁系统,在各向同性Heisenberg极限下,系统存在有限温度的相变,并计算了系统的序参量和临界指数; 对于反铁磁系统,在各向同性Heisenberg极限下,临界温度不等于零,在临界线上不存在重入行为.     

A frustrated heisenberg antiferromagnet on a triangular lattice with next-nearest neighbor interactions

Using the Monte Carlo method, we study the critical properties of the three-dimensional frustrated Heisenberg model on a triangular lattice with allowance for next-nearest neighbor interactions. Using the theory of finite-size scaling, we calculate the static magnetic and chiral critical exponents of heat capacity α, susceptibility γ, γ _k , magnetization β, β _k , and correlation length ν.     

Phase transitions in the antiferromagnetic Heisenberg model on a layered triangular lattice with the next-nearest neighbor interactions

Phase transitions in the three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice with the next-nearest neighbor interactions have been studied by the histogram Monte Carlo method. Phase transitions in this model have been studied in the range of the next-nearest neighbor interactions from 0.0 to 1.0. The first-order phase transition has been revealed in the considered interval in the studied model.     

Phase diagram of frustrated mixed-spin ladders in the strong-coupling limit

We study the ground-state properties of frustrated Heisenberg ferrimagnetic ladders with antiferromagnetic exchange interactions and two types of alternating sublattice spins. In the limit of strong rung couplings, we show that the mixed spin-1/2 and spin-1 ladders can be systematically mapped onto a spin-1/2 Heisenberg model with additional next-nearest-neighbor exchanges. The system is either in a ferrimagnetic state or in a critical spin-liquid state depending on the competition between the spin exchanges along the legs and the diagonal exchanges.